Generating representations of input sequences using neural networks

ABSTRACT

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for generating representations of input sequences. One of the methods includes obtaining an input sequence, the input sequence comprising a plurality of inputs arranged according to an input order; processing the input sequence using a first long short term memory (LSTM) neural network to convert the input sequence into an alternative representation for the input sequence; and processing the alternative representation for the input sequence using a second LSTM neural network to generate a target sequence for the input sequence, the target sequence comprising a plurality of outputs arranged according to an output order.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Application No.62/009,121, filed on Jun. 6, 2014. The disclosure of the priorapplication is considered part of and is incorporated by reference inthe disclosure of this application.

BACKGROUND

This specification relates to generating representations of inputsequences using neural networks.

Many data processing tasks involve converting an ordered sequence ofinputs into an ordered sequence of outputs. For example, machinetranslation systems translate an input sequence of words in one languageinto a sequence of words in another language. As another example,pronunciation systems convert an input sequence of graphemes into atarget sequence of phonemes.

SUMMARY

This specification describes how a system implemented as computerprograms on one or more computers in one or more locations can convertan input sequence into a target sequence that is a representation of theinput sequence, e.g., a representation of the input sequence in adifferent form.

Particular embodiments of the subject matter described in thisspecification can be implemented so as to realize one or more of thefollowing advantages. A target sequence that is a representation of aninput sequence in a different form can be accurately predicted. Forexample, a machine translation system can accurately predict thetranslation for a received sequence of words. As another example, agrapheme-to-phoneme system can accurately predict the sequence ofphonemes that represents a received grapheme sequence. As anotherexample, an autoencoder system can accurately autoencode a receivedsequence.

The details of one or more embodiments of the subject matter describedin this specification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example sequence representation system.

FIG. 2 is a flow diagram of generating a target representation of aninput sequence.

FIG. 3 is a flow diagram of an example process for generating a targetsequence using a decoder LSTM neural network.

FIG. 4 is a flow diagram of an example process for performing a beamsearch decoding using a decoder LSTM neural network.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

FIG. 1 shows an example sequence representation system 100. The sequencerepresentation system 100 is an example of a system implemented ascomputer programs on one or more computers in one or more locations, inwhich the systems, components, and techniques described below can beimplemented.

The sequence representation system 100 receives input sequences andconverts the input sequences to target sequences. Each target sequenceis a representation of the input sequence, e.g., a representation of theinput sequence in a different form. For example, the sequencerepresentation system 100 can receive an input sequence 102 and generatea target sequence 122 for the input sequence 102. The target sequence122 for the input sequence 102 is an ordered sequence of outputs thatthe sequence representation system 100 has classified as representingthe input sequence. For example, if the input sequence 102 is a sequenceof words in an original language, e.g., a sentence or phrase, the targetsequence 122 generated by the sequence representation system 100 may bea translation of the input sequence into a target language, i.e., asequence of words in the target language that represents the sequence ofwords in the original language. As another example, if the inputsequence 102 is a sequence of graphemes, e.g., the sequence {g, o, o, g,l, e}, the target sequence 122 generated by the sequence representationsystem 100 may be a phoneme representation of the input sequence, e.g.,the sequence {g, uh, g, ax, l}.

Generally, the input sequences received by the sequence representationsystem 100 and the target sequences generated by the sequencerepresentation system 100 are variable-length sequences, i.e., sequencesthat can contain varying numbers of inputs and outputs, respectively.Additionally, the number of outputs in a target sequence generated bythe sequence representation system 100 may be the same as or differentfrom the number of inputs in the input sequence from which the targetsequence was generated.

The sequence representation system 100 includes an encoder longshort-term memory (LSTM) neural network 110 and a decoder LSTM neuralnetwork 120.

As part of generating a target sequence from an input sequence, thesequence representation system 100 processes the input sequence usingthe encoder LSTM neural network 110 to generate an alternativerepresentation for the input sequence, e.g., an alternativerepresentation 112 for the input sequence 102.

The encoder LSTM neural network 110 is a recurrent neural network thatreceives an input sequence and generates an alternative representationfrom the input sequence. In particular, the encoder LSTM neural network110 is an LSTM neural network that includes one or more LSTM neuralnetwork layers, with each of the LSTM layers including one or more LSTMmemory blocks. Each LSTM memory block can include one or more cells thateach include an input gate, a forget gate, and an output gate that allowthe cell to store previous activations generated by the cell, e.g., as ahidden state for use in generating a current activation or to beprovided to other components of the LSTM neural network 110. An exampleLSTM neural network is described in more detail in “Generating sequenceswith recurrent neural networks,” Alex Graves, available at arxiv.org.

The encoder LSTM neural network 110 has been configured, e.g., throughtraining, to process each input in a given input sequence to generatethe alternative representation of the input sequence in accordance witha set of parameters. In particular, the encoder LSTM neural network 110is configured to receive each input in the input sequence in the inputorder and, for a given received input, to update the current hiddenstate of the encoder LSTM neural network 110 by processing the receivedinput, i.e., to modify the current hidden state of the encoder LSTMneural network 110 that has been generated by processing previous inputsfrom the input sequence by processing the current received input.

Generating an alternative representation using the encoder LSTM neuralnetwork is described in more detail below with reference to FIG. 2.

The sequence representation system 100 processes the generatedalternative representation of the input sequence using the decoder LSTMneural network 120 to generate the target sequence for the inputsequence. For example, the sequence representation system 100 canprocess the alternative representation 112 using the decoder LSTM neuralnetwork 120 to generate the target sequence 122 for the input sequence102.

The decoder LSTM neural network 120 is an LSTM neural network thatincludes one or more LSTM layers and that is configured receive acurrent output in a target sequence and to generate a respective outputscore for each of a set of possible outputs from the current output andin accordance with the current hidden state of the decoder LSTM neuralnetwork 120 and current values of a set of parameters. The output scorefor a given output represents the likelihood that the output is the nextoutput in the target sequence, i.e., that the output immediately followsthe current output in the target sequence. As part of generating theoutput scores, the decoder LSTM neural network 120 also updates thehidden state of the network to generate an updated hidden state.

The set of possible outputs includes a vocabulary of possible outputsand a designated end-of-sentence token. The outputs in the vocabulary ofoutputs are outputs that have been provided to the system as beingpossible representations of inputs received by the system, e.g., wordsin a target language if inputs to the system are words in an originallanguage and the system translates input sequences from the originallanguage to the target language, phonemes if inputs to the system aregraphemes and the system generates phoneme representations of graphemesequences, or that includes each possible input to the system if thesystem is an autoencoder. The end-of-sentence token is a designatedoutput that is not in the vocabulary of possible outputs.

Processing an alternative representation using the decoder LSTM neuralnetwork to generate a target sequence is described in more detail belowwith reference to FIGS. 2 and 3.

FIG. 2 is a flow diagram of an example process 200 for generating atarget sequence from an input sequence. For convenience, the process 200will be described as being performed by a system of one or morecomputers located in one or more locations. For example, a sequencerepresentation system, e.g., the sequence representation system 100 ofFIG. 1, appropriately programmed, can perform the process 200.

The system obtains an input sequence (step 202). The input sequenceincludes a set of inputs arranged according to an input order. Forexample, the input sequence may be a sequence of graphemes to beconverted into a corresponding sequence of phonemes or a sequence ofwords in one language to be translated into a sequence of words in adifferent language.

The system processes the input sequence using an encoder LSTM neuralnetwork, e.g., the encoder LSTM neural network 110 of FIG. 1, to convertthe input sequence into an alternative representation for the inputsequence (step 204).

As part of processing the input sequence, the system modifies the inputsequence to insert the end-of-sentence token or a different designatedtoken at the end of the input sequence, i.e., after the input in thelast position of the input order, to generate a modified input sequence.The designated token is a designated input that is not in a vocabularyof possible inputs that may be included in input sequences processed bythe system and, if the designated token is the end-of-sentence token, isalso not in the vocabulary of possible outputs.

The system then processes each input in the modified input sequenceusing the encoder LSTM neural network to generate the alternativerepresentation for the input sequence. In particular, the systemgenerates the alternative representation from the hidden state of theencoder LSTM neural network. For example, the alternative representationmay be the hidden state of the encoder LSTM after the designated tokenat the end of the input sequence has been processed, i.e., the lasthidden state of the encoder LSTM. Thus, because the system generates thealternative representation from the hidden state of the encoder LSTMneural network, the alternative representation of the input sequence isa fixed-length representation, i.e., the number of elements in thealternative representation is fixed and is not dependent on the numberof inputs in the input sequence. For example, the LSTM hidden state and,accordingly, the alternative representation may be a vector of numericvalues that has a fixed dimensionality, e.g., a vector of floating pointvalues or of quantized representations of floating point values.

The system processes the alternative representation using a decoder LSTMneural network, e.g., the decoder LSTM neural network 120 of FIG. 1, togenerate a target sequence for the input sequence (step 206). The targetsequence is a sequence of outputs arranged according to an output order.

Generally, the system processes the alternative representation using thedecoder LSTM neural network by initializing an initial hidden state ofthe decoder LSTM to the alternative representation of the inputsequence, i.e., setting the initial state hidden state equal to thealternative representation.

For example, in the context where the system is configured to receive aninput sequence of words in an original language and to generate a targetsequence of words in a target language that is a translation of thewords in the input sequence into the target language, the system canreceive an input sequence of words in the original language and add thedesignated token at the end of the input sequence. The system can thenprocess the modified input sequence using the encoder LSTM neuralnetwork to generate an alternative representation of the input sequenceand process the alternative representation using the decoder LSTM neuralnetwork to generate a target sequence of words in the target languagethat is a translation of the input sequence into the target language.

FIG. 3 is a flow diagram of an example process 300 for generating atarget sequence using a decoder LSTM neural network. For convenience,the process 300 will be described as being performed by a system of oneor more computers located in one or more locations. For example, asequence representation system, e.g., the sequence representation system100 of FIG. 1, appropriately programmed, can perform the process 300.

The system initializes the initial hidden state of the decoder LSTMneural network to the alternative representation of the input sequence(step 302).

The system generates a set of initial output scores using the decoderLSTM neural network in accordance with the initial hidden state (step304). That is, the system processes an initial placeholder output, e.g.,an output that is all zeroes, using the decoder LSTM neural network inaccordance with the initial hidden state to generate the initial outputscores and to generate an updated hidden state using the initial hiddenstate.

The system selects a highest-scoring output according to the initialoutput scores as the first output in the target sequence (step 306).

The system processes the selected output using the decoder LSTM neuralnetwork to generate a set of next output scores (step 308). That is, thesystem processes the selected output in accordance with the updatehidden state of the network to generate the set of next output scoresand to again update the hidden state of the network. Because the hiddenstate of the network is updated at each output time step, the networkdoes not re-process the alternative representation of the input sequenceto generate each output in the output sequence. Rather, the alternativerepresentation of the input sequence is used only to initialize thedecoder LSTM network before the first output is generated.

The system selects a highest-scoring output according to the next outputscores as the next output in the target sequence (step 310).

The system can repeat steps 308 and 310 to add outputs to the targetsequence and to update the hidden state of the network until thehighest-scoring output is the end-of-sentence token rather than one ofthe outputs from the vocabulary of outputs. The system can thenconsider, as the target sequence, the sequence of the selected outputsthat were selected prior to the end-of-sentence token being thehighest-scoring output.

In some implementations, the system generates multiple possible targetsequences and determines a respective sequence score for each possibletarget sequence. The system can then select the possible target sequencehaving the highest sequence score as the target sequence. In particular,the system can generate the possible target sequences by performing abeam search decoding using the decoder LSTM neural network.

FIG. 4 is a flow diagram of an example process 400 for performing a beamsearch decoding using a decoder LSTM neural network. For convenience,the process 400 will be described as being performed by a system of oneor more computers located in one or more locations. For example, asequence representation system, e.g., the sequence representation system100 of FIG. 1, appropriately programmed, can perform the process 400.

The system initializes the initial hidden state of the decoder LSTMneural network to the alternative representation of the input sequence(step 402).

The system generates the set of initial output scores using the decoderLSTM neural network in accordance with the initial hidden state (step404).

The system selects a predetermined number of highest-scoring possibleoutputs according to the initial scores (step 406). The system generatesa respective possible target sequence for each selected possible output,each possible target sequence including the corresponding selectedpossible output at the first position in the output order. The systemassociates the possible target sequence with the initial score for thecorresponding possible output as the sequence score for the possibletarget sequence.

The system generates a respective set of output scores for eachmaintained possible target sequence for the current position in theoutput order (step 408). That is, for each maintained possible targetsequence, the system processes the current output in the possible targetsequence using the decoder LSTM neural network to generate a set ofoutput scores in accordance with the current hidden state of the decoderLSTM neural network for the possible output sequence. The set of outputscores includes a respective output score for each of the set ofpossible outputs. The system processes each maintained possible targetsequence independently from each other maintained possible targetsequence, so that the hidden state of the decoder LSTM used to generatethe set of output scores for the current output in a given possibletarget sequence is based only on the processing of the possible targetsequence and not on the selected outputs for any other possible targetsequence.

For example, once the system has selected the possible outputs for thefirst position in the output order, the system can process each of theselected first position outputs using the decoder LSTM neural network togenerate a respective set of output scores for each selected firstposition output.

The system generates, for each maintained possible target sequence, arespective sequence score for each possible candidate target sequencethat can be generated from the possible target sequence (step 410). Acandidate target sequence for a given possible target sequence is asequence that appends one of the possible outputs to the end of thepossible target sequence. The sequence score for the candidate targetsequence is the sequence score for the possible target sequencemultiplied by the output score for the appended possible output.

The system selects the predetermined number of candidate targetsequences that have the highest sequence scores (step 412).

The system updates the maintained possible target sequences to be theselected candidate target sequences (step 414).

When a selected candidate target sequence ends with the end-of-sentencetoken, the system removes the selected candidate target sequence fromthe beam, i.e., stops adding additional outputs to the selectedcandidate target sequence, and considers the selected candidate targetsequence prior to the end-of-sentence token being added to be a finalpossible target sequence. The system also reduces the predeterminednumber of sequences to be maintained by one.

The system can repeat steps 408-414 of the process 400 until eachmaintained possible target sequence has been finalized. The system canthen select the final possible target sequence having the highestsequence score as the target sequence for the input sequence or canprovide multiple ones of the final possible target sequences as possibletarget sequences for the input sequence.

In order to configure the encoder LSTM neural network and the decoderLSTM neural network, the system can train the networks usingconventional machine learning training techniques, e.g., usingStochastic Gradient Descent. In particular, the system can train thenetworks jointly by backpropagating gradients computed for the decoderLSTM neural network back to the encoder LSTM neural network to adjustthe values of the parameters of the encoder LSTM neural network duringthe training technique.

Embodiments of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly-embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Embodiments of the subject matter described in thisspecification can be implemented as one or more computer programs, i.e.,one or more modules of computer program instructions encoded on atangible non transitory program carrier for execution by, or to controlthe operation of, data processing apparatus. Alternatively or inaddition, the program instructions can be encoded on an artificiallygenerated propagated signal, e.g., a machine-generated electrical,optical, or electromagnetic signal, that is generated to encodeinformation for transmission to suitable receiver apparatus forexecution by a data processing apparatus. The computer storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofone or more of them.

The term “data processing apparatus” encompasses all kinds of apparatus,devices, and machines for processing data, including by way of example aprogrammable processor, a computer, or multiple processors or computers.The apparatus can include special purpose logic circuitry, e.g., an FPGA(field programmable gate array) or an ASIC (application specificintegrated circuit). The apparatus can also include, in addition tohardware, code that creates an execution environment for the computerprogram in question, e.g., code that constitutes processor firmware, aprotocol stack, a database management system, an operating system, or acombination of one or more of them.

A computer program (which may also be referred to or described as aprogram, software, a software application, a module, a software module,a script, or code) can be written in any form of programming language,including compiled or interpreted languages, or declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A computer program may, butneed not, correspond to a file in a file system. A program can be storedin a portion of a file that holds other programs or data, e.g., one ormore scripts stored in a markup language document, in a single filededicated to the program in question, or in multiple coordinated files,e.g., files that store one or more modules, sub programs, or portions ofcode. A computer program can be deployed to be executed on one computeror on multiple computers that are located at one site or distributedacross multiple sites and interconnected by a communication network.

The processes and logic flows described in this specification can beperformed by one or more programmable computers executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Computers suitable for the execution of a computer program include, byway of example, can be based on general or special purposemicroprocessors or both, or any other kind of central processing unit.Generally, a central processing unit will receive instructions and datafrom a read only memory or a random access memory or both. The essentialelements of a computer are a central processing unit for performing orexecuting instructions and one or more memory devices for storinginstructions and data. Generally, a computer will also include, or beoperatively coupled to receive data from or transfer data to, or both,one or more mass storage devices for storing data, e.g., magnetic,magneto optical disks, or optical disks. However, a computer need nothave such devices. Moreover, a computer can be embedded in anotherdevice, e.g., a mobile telephone, a personal digital assistant (PDA), amobile audio or video player, a game console, a Global PositioningSystem (GPS) receiver, or a portable storage device, e.g., a universalserial bus (USB) flash drive, to name just a few.

Computer readable media suitable for storing computer programinstructions and data include all forms of non-volatile memory, mediaand memory devices, including by way of example semiconductor memorydevices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks,e.g., internal hard disks or removable disks; magneto optical disks; andCD ROM and DVD-ROM disks. The processor and the memory can besupplemented by, or incorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube) or LCD (liquidcrystal display) monitor, for displaying information to the user and akeyboard and a pointing device, e.g., a mouse or a trackball, by whichthe user can provide input to the computer. Other kinds of devices canbe used to provide for interaction with a user as well; for example,feedback provided to the user can be any form of sensory feedback, e.g.,visual feedback, auditory feedback, or tactile feedback; and input fromthe user can be received in any form, including acoustic, speech, ortactile input. In addition, a computer can interact with a user bysending documents to and receiving documents from a device that is usedby the user; for example, by sending web pages to a web browser on auser's client device in response to requests received from the webbrowser.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front end component, e.g., aclient computer having a graphical user interface or a Web browserthrough which a user can interact with an implementation of the subjectmatter described in this specification, or any combination of one ormore such back end, middleware, or front end components. The componentsof the system can be interconnected by any form or medium of digitaldata communication, e.g., a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), e.g., the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or of what may be claimed, but rather as descriptions offeatures that may be specific to particular embodiments of particularinventions. Certain features that are described in this specification inthe context of separate embodiments can also be implemented incombination in a single embodiment. Conversely, various features thatare described in the context of a single embodiment can also beimplemented in multiple embodiments separately or in any suitablesubcombination. Moreover, although features may be described above asacting in certain combinations and even initially claimed as such, oneor more features from a claimed combination can in some cases be excisedfrom the combination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various system modulesand components in the embodiments described above should not beunderstood as requiring such separation in all embodiments, and itshould be understood that the described program components and systemscan generally be integrated together in a single software product orpackaged into multiple software products.

Particular embodiments of the subject matter have been described. Otherembodiments are within the scope of the following claims. For example,the actions recited in the claims can be performed in a different orderand still achieve desirable results. As one example, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In certain implementations, multitasking and parallelprocessing may be advantageous.

What is claimed is:
 1. A method performed by one or more computers, themethod comprising: obtaining an input sequence, the input sequencecomprising a plurality of inputs arranged according to an input order;processing the input sequence using a first long short term memory(LSTM) neural network to convert the input sequence into an alternativerepresentation for the input sequence; and processing the alternativerepresentation for the input sequence using a second LSTM neural networkto generate a target sequence for the input sequence, the targetsequence comprising a plurality of outputs arranged according to anoutput order.
 2. The method of claim 1, wherein the input sequence is avariable length input sequence.
 3. The method of claim 2, wherein thealternative representation is a vector of fixed dimensionality.
 4. Themethod of claim 1, wherein processing the input sequence comprises:adding an end-of-sentence token to the end of the input sequence togenerate a modified input sequence; and processing the modified inputsequence using the first LSTM neural network.
 5. The method of claim 1,wherein processing the alternative representation for the input sequenceusing the second LSTM neural network comprises initializing a hiddenstate of the second LSTM neural network to the alternativerepresentation for the input sequence.
 6. The method of claim 5, whereinprocessing the alternative representation for the input sequence usingthe second LSTM neural network comprises: processing the alternativerepresentation for the input sequence using the second LSTM neuralnetwork to generate a respective sequence score for each of a set ofpossible target sequences; and selecting a possible target sequencehaving a highest sequence score as the target sequence for the inputsequence.
 7. The method of claim 6, wherein the set of possible targetsequences comprises possible target sequences of varying lengths.
 8. Themethod of claim 6, wherein processing the alternative representation forthe input sequence using the second LSTM neural network comprises:processing the alternative representation using the second LSTM neuralnetwork using a left to right beam search decoding.
 9. The method ofclaim 1, further comprising: training the first LSTM neural network andthe second LSTM neural network using Stochastic Gradient Descent. 10.The method of claim 1, wherein the input sequence is a sequence of wordsin a first language and the target sequence is a translation of thesequence of words into a second language.
 11. The method of claim 1,wherein the input sequence is a sequence of words and the targetsequence is an autoencoding of the input sequence.
 12. The method ofclaim 1, wherein the input sequence is a sequence of graphemes and thetarget sequence is a phoneme representation of the sequence ofgraphemes.
 13. A system comprising one or more computers and one or morestorage devices storing instructions that when executed by the one ormore computers cause the one or more computers to perform operationscomprising: obtaining an input sequence, the input sequence comprising aplurality of inputs arranged according to an input order; processing theinput sequence using a first long short term memory (LSTM) neuralnetwork to convert the input sequence into an alternative representationfor the input sequence; and processing the alternative representationfor the input sequence using a second LSTM neural network to generate atarget sequence for the input sequence, the target sequence comprising aplurality of outputs arranged according to an output order.
 14. Thesystem of claim 13, wherein the input sequence is a variable lengthinput sequence.
 15. The system of claim 14, wherein the alternativerepresentation is a vector of fixed dimensionality.
 16. The system ofclaim 13, wherein processing the alternative representation for theinput sequence using the second LSTM neural network comprisesinitializing a hidden state of the second LSTM neural network to thealternative representation for the input sequence.
 17. The system ofclaim 16, wherein processing the alternative representation for theinput sequence using the second LSTM neural network comprises:processing the alternative representation for the input sequence usingthe second LSTM neural network to generate a respective sequence scorefor each of a set of possible target sequences; and selecting a possibletarget sequence having a highest sequence score as the target sequencefor the input sequence.
 18. The system of claim 17, wherein the set ofpossible target sequences comprises possible target sequences of varyinglengths.
 19. The system of claim 17, wherein processing the alternativerepresentation for the input sequence using the second LSTM neuralnetwork comprises: processing the alternative representation using thesecond LSTM neural network using a left to right beam search decoding.20. A computer program product encoded on one or more non-transitorystorage media, the computer program product comprising instructions thatwhen executed by the one or more computers cause the one or morecomputers to perform operations comprising: obtaining an input sequence,the input sequence comprising a plurality of inputs arranged accordingto an input order; processing the input sequence using a first longshort term memory (LSTM) neural network to convert the input sequenceinto an alternative representation for the input sequence; andprocessing the alternative representation for the input sequence using asecond LSTM neural network to generate a target sequence for the inputsequence, the target sequence comprising a plurality of outputs arrangedaccording to an output order.
 21. The method of claim 1, whereinprocessing the alternative representation for the input sequence usingthe second LSTM neural network to generate the target sequencecomprises: generating an initial output for an initial position of thetarget sequence by: (i) initializing a hidden state of the second LSTMneural network to the alternative representation for the input sequence,and (ii) processing a placeholder output according to the initializedhidden state of the second LSTM neural network to generate the initialoutput for the initial position of the target sequence, wherein thehidden state of the second LSTM neural network updates from theinitialized hidden state as a result of processing the placeholderoutput; and generating one or more subsequent outputs for subsequentpositions of the target sequence following the initial position,including for each subsequent output processing a preceding output froma preceding position of the target sequence according to a currenthidden state of the second LSTM neural network to generate thesubsequent output, wherein the hidden state of the second LSTM neuralnetwork updates from the current hidden state as a result of processingthe preceding output.
 22. The method of claim 1, wherein processing thealternative representation for the input sequence using the second LSTMneural network to generate the target sequence comprises: initializing ahidden state of the second LSTM neural network to the alternativerepresentation for the input sequence to generate an initial output ofthe target sequence; and generating subsequent outputs of the targetsequence following the initial output without re-processing thealternative representation for the input sequence using the second LSTMneural network.